1. Introduction The repudiation of infinity, or horror infiniti, has generally been considered as an insignia of ancient culture. (For a general introduction to the topic, see e.g. Moore 1993, Moore 1990, Maor 1987, de Vogel 1959, and Cohn 1896.) In the same vein it is usually argued that a significant change occurred in the attitude to infinity at the beginning of the Christian era and its newborn religion. As Christians made an attempt to buttress their revelatory experience of God also on the level of rationality, relying in this action on the rich philosophical heritage of the ancients, there was introduced a kind of clash between finitist and infinitist elements into the thought structure of the Christian world. I would like to argue that this substantial conflict provides us with contextual means for investigating not only the concept of theological infinity, elaborated in the Middle Ages, but enables us to look in a historically consecutive way also at the two modern children of infinity - at the idea of physical infinity, starting to emerge in the Renaissance, and at aesthetic infinity, appearing in the second half of the 18th century. In other words, I claim that the history of infinity offers us scope by which to analyze the mutually instigating relationship among faith, knowledge and artistic representation: it reveals how a certain idea, accepted on the grounds of religious arguments, can force the modification of the speculative system of the age and lead, in terms of the modern era, to the foundation of new scientific (experimental) truths, as well as of a new system of artistic representation. Keeping in sight such a project of cultural rhetoric of infinity, I will confine myself in the present article to the topic of the revaluation of infinity in late antiquity and early Christianity. 2. Platonic-Aristotelian concept of infinity Before going on to tackle the proper subject of the paper, it is necessary to offer some explanatory remarks about the Greeks' disgust of infinity. First, we should make it clearer what we mean by the word infinity because its usual Greek equivalent, apeiron, had a range of meanings not necessarily identical with our sense of the word (Guthrie 1962:83-89, Sweeney 1992:15-28). For example, it is questionable how much we can attribute to it the strictly spatial connotations prevalent in our perception. Aristotle had stated that the belief in the existence of infinity can be motivated in us by five different impressions producing the respective modes of infinity: temporal eternity, infinite divisibility of quantities, the endless process of generation and perishing, the absence of a final boundary line in the corporeal world, the additive infinity in numbers and in our thought (Physics 203b16-269); some steps further Aristotle comes to conclude that infinity as such can exist either by way of addition or by way of division (Physics 204a6-8). As to Aristotle's personal conception of infinity, he coupled it, as is well known, with potentiality pertinent to matter, admitting, quite interestingly, the possibility of endless division as regards spatial quantity, while denying the infinity in space by means of addition (which, i.e. additive infinity, he was in turn ready to admit in respect to time) (Moore 1990: 40-41). In spite of the subtleties we have to consider in speaking about apeiron in various Greek philosophers, I would wish for the moment to stay on the more general plane and to declare simply that the so-called Greek abhorrence of infinity refers to the lowest position infinity as indefiniteness necessarily held, as compared to all finitist conceptions, in traditional Greek thought. In other words, not before Christianity and Neoplatonism (Plotinus), was infinity assigned in the Greek mind a significant cognitive value, let alone elevating it to the position of highest perfection. Nevertheless, even this broad statement needs some qualifications and can be maintained only with the proviso that we limit our scope of vision chiefly to the mainstream of ancient philosophy, i. …
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Dec 1, 2016
Yinyin Wu + 1
